Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2021
Hard
A single-jet Pelton wheel operates at 300 rpm with mean wheel diameter 2 m. Water leaves the jet at 40 m/s with flow rate 5 m³/s. The jet is deflected by the bucket through 165°. Neglecting all losses, the power developed by the Pelton wheel is ___ MW (round off to two decimal places).
2.65 MW(± 0.2 accepted)
Explanation
Bucket speed U=πDN/60=π×2×300/60≈31.42 m/s. Deflection 165° means the bucket-exit angle from the reverse jet direction is β=180-165=15°. Power=ρQ(V-U)(1+cosβ)U=1000×5×(40-31.42)×(1+cos15°)×31.42≈2.65×10⁶ W=2.65 MW.
Source: GATE ME 2021 Session 1 (ME-1) (2021)
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